16,155 research outputs found
On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators
The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined
Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory
We continue the investigation of massive integrable models by means of the
bootstrap fusion procedure, started in our previous work on O(3) nonlinear
sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear
sigma model we prove a similar relation between sine-Gordon theory and a
one-parameter deformation of the O(3) sigma model, the sausage model. This
allows us to write down a free field representation for the
Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral
representation for the generating functions of form-factors in this theory. We
also clear up the origin of the singularities in the bootstrap construction and
the reason for the problem with the kinematical poles.Comment: 16 pages, revtex; references added, some typos corrected. Accepted
for publication in Physical Review
Free field representation for the O(3) nonlinear sigma model and bootstrap fusion
The possibility of the application of the free field representation developed
by Lukyanov for massive integrable models is investigated in the context of the
O(3) sigma model. We use the bootstrap fusion procedure to construct a free
field representation for the O(3) Zamolodchikov- Faddeev algebra and to write
down a representation for the solutions of the form-factor equations which is
similar to the ones obtained previously for the sine-Gordon and SU(2) Thirring
models. We discuss also the possibility of developing further this
representation for the O(3) model and comment on the extension to other
integrable field theories.Comment: 14 pages, latex, revtex v3.0 macro package, no figures Accepted for
publication in Phys. Rev.
Modes of magnetic resonance of S=1 dimer chain compound NTENP
The spin dynamics of a quasi one dimensional bond alternating spin-gap
antiferromagnet Ni(CHN)NO(ClO) (abbreviated as NTENP) is
studied by means of electron spin resonance (ESR) technique. Five modes of ESR
transitions are observed and identified: transitions between singlet ground
state and excited triplet states, three modes of transitions between spin
sublevels of collective triplet states and antiferromagnetic resonance
absorption in the field-induced antiferromagnetically ordered phase.
Singlet-triplet and intra-triplet modes demonstrate a doublet structure which
is due to two maxima in the density of magnon states in the low-frequency
range. A joint analysis of the observed spectra and other experimental results
allows to test the applicability of the fermionic and bosonic models. We
conclude that the fermionic approach is more appropriate for the particular
case of NTENP.Comment: 11 pages, 11 figures, published in Phys.Rev.
Four-Loop Cusp Anomalous Dimension From Obstructions
We introduce a method for extracting the cusp anomalous dimension at L loops
from four-gluon amplitudes in N=4 Yang-Mills without evaluating any integrals
that depend on the kinematical invariants. We show that the anomalous dimension
only receives contributions from the obstructions introduced in hep-th/0601031.
We illustrate this method by extracting the two- and three-loop anomalous
dimensions analytically and the four-loop one numerically. The four-loop result
was recently guessed to be f^4 = - (4\zeta^3_2+24\zeta_2\zeta_4+50\zeta_6-
4(1+r)\zeta_3^2) with r=-2 using integrability and string theory arguments in
hep-th/0610251. Simultaneously, f^4 was computed numerically in hep-th/0610248
from the four-loop amplitude obtaining, with best precision at the symmetric
point s=t, r=-2.028(36). Our computation is manifestly s/t independent and
improves the precision to r=-2.00002(3), providing strong evidence in favor of
the conjecture. The improvement is possible due to a large reduction in the
number of contributing terms, as well as a reduction in the number of
integration variables in each term.Comment: 23 pages, revtex; v2,v3: minor typos fixed and references adde
Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk
The conjecture that the scaling limit of the two-dimensional self-avoiding
walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE)
with leads to explicit predictions about the SAW. A remarkable
feature of these predictions is that they yield not just critical exponents,
but probability distributions for certain random variables associated with the
self-avoiding walk. We test two of these predictions with Monte Carlo
simulations and find excellent agreement, thus providing numerical support to
the conjecture that the scaling limit of the SAW is SLE.Comment: TeX file using APS REVTeX 4.0. 10 pages, 5 figures (encapsulated
postscript
Soliton form factors from lattice simulations
The form factor provides a convenient way to describe properties of
topological solitons in the full quantum theory, when semiclassical concepts
are not applicable. It is demonstrated that the form factor can be calculated
numerically using lattice Monte Carlo simulations. The approach is very general
and can be applied to essentially any type of soliton. The technique is
illustrated by calculating the kink form factor near the critical point in
1+1-dimensional scalar field theory. As expected from universality arguments,
the result agrees with the exactly calculable scaling form factor of the
two-dimensional Ising model.Comment: 5 pages, 3 figures; v2: discussion extended, references added,
version accepted for publication in PR
Single photonics at telecom wavelengths using nanowire superconducting detectors
Single photonic applications - such as quantum key distribution - rely on the
transmission of single photons, and require the ultimate sensitivity that an
optical detector can achieve. Single-photon detectors must convert the energy
of an optical pulse containing a single photon into a measurable electrical
signal. We report on fiber-coupled superconducting single-photon detectors
(SSPDs) with specifications that exceed those of avalanche photodiodes (APDs),
operating at telecommunication wavelength, in sensitivity, temporal resolution
and repetition frequency. The improved performance is demonstrated by measuring
the intensity correlation function g(2)(t) of single-photon states at 1300nm
produced by single semiconductor quantum dots (QDs).Comment: 7 pages, 5 figures - submitted 12 OCT 200
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